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## Distributions of polynomials on multidimensional and infinite-dimensional spaces with measures

New results on distributions of polynomials on multidimensional and infinite-dimensional spaces with measures are obtained

The paper presents** **the approach for multi-dimensional analysis of marketing tactics of the companies employing network tools. The research suggests onmi-channel distribution tactic of a company as a node in eight-dimensional space. Dimensions for node location are defined by frequency of usage of eight communication channels (friends, acquaintances, telephone, home presentations, printed advertisement, internet, e-mail, door-to-door). The comparison is grounded on measuring pairwise distance between nodes in eight-dimensional space. Pairwise distance measured by Euclidian norm is used as a weight of edge between companies. The smaller the Euclidean distance, the higher is similarity. Further we employ network representation of multidimensional statistics to analyze performance and companies’ characteristic, such as product category, market share, education level and average age of distributors. Empirical implication is approved on the sample from 5694 distributors from sixteen (16) fast moving consumer goods (FMCG) distributing companies from direct selling industry.

The article examines conceptual problems of Distribution Logistics in view of realization of the «Distribution Management» function and the design of an effective logistical distribution network of a goods flow. Distribution Management demands logistics to have a constant control over the efficiency of organization of logistical processes in a distribution network. To increase efficiency of distribution network operation there should be a careful and all round assessment of the existing and perspective condition of a company’s distribution systems. The purpose of this effectiveness assessment of distribution systems of a company is to

thoroughly study the organization of logistical processes in the system, condition and operation control of a goods movement system and logistics operations costs and functions in distribution, and to reveal defects in organization, performance and control of logistical activities. The author considers interaction of logistics and adjacent company’s departments while managing distribution. Several unique algorithms of designing and reengineering of a distribution network are offered and it is shown in the case studies how they are realized.

The article shows that in the context of severe competition and an increasing expansion of Western firms issues of an effective collaboration of Logistics and Marketing become more and more important for most Russian companies. It is demonstrated that organization of Marketing and Logistics collaboration has changed significantly in many companies lately – from the traditional scheme of functional division of a firm’s fields of activity to general costs optimization and finding the balance of “logistics service costs/quality” in distribution. The author systematically examines spheres of Marketing and Logistics collaboration and provides a detailed characteristics of marketing channels formation strategies with regard to Logistics requirements. Main trends of Logistics activities in the context of realization of a company’s marketing channels formation strategies are explored.

It is shown, that recently among technologies of integration of contractors at supply chains «Vendor managed inventory» concept has been growing in popularity (VMI). Basic definitions within the framework of this concept/technology are analysed. VMI technology is viewed within the confines of development of logistics and supply chain management, and are estimated those benefits, which can be derived (on the example of distributing system). Basic aspects are distinguished and analyzed, which are necessary to be defined while taking decision of implementing VMI programme. These key elements are: inventory emplacement, level of inventory monitoring and information transparency, stock replenishment system and property rights on inventory. Comparing characteristic of VMI and consignment is given. Advantages and disadvantages of technology for supplier and consumer are given. Practical aspects of introducing VMI into the company – distributor of spare parts to constructive road equipment are viewed.

Abstract—On the basis of logical-probabilistic approach proposed risk model successful attacks on social media on the Internet in terms of information warfare. We formulated and investigated the criterion of decision-making framework to achieve the goals of information warfare. Proposed algorithmic foundations of the developed criteria in Hadoop cluster.

Business Enlish practice tasks and texts for the development and mastering of Business English Vocabulary.

Let k be a field of characteristic zero, let G be a connected reductive algebraic group over k and let g be its Lie algebra. Let k(G), respectively, k(g), be the field of k- rational functions on G, respectively, g. The conjugation action of G on itself induces the adjoint action of G on g. We investigate the question whether or not the field extensions k(G)/k(G)^G and k(g)/k(g)^G are purely transcendental. We show that the answer is the same for k(G)/k(G)^G and k(g)/k(g)^G, and reduce the problem to the case where G is simple. For simple groups we show that the answer is positive if G is split of type A_n or C_n, and negative for groups of other types, except possibly G_2. A key ingredient in the proof of the negative result is a recent formula for the unramified Brauer group of a homogeneous space with connected stabilizers. As a byproduct of our investigation we give an affirmative answer to a question of Grothendieck about the existence of a rational section of the categorical quotient morphism for the conjugating action of G on itself.

Let G be a connected semisimple algebraic group over an algebraically closed field k. In 1965 Steinberg proved that if G is simply connected, then in G there exists a closed irreducible cross-section of the set of closures of regular conjugacy classes. We prove that in arbitrary G such a cross-section exists if and only if the universal covering isogeny Ĝ → G is bijective; this answers Grothendieck's question cited in the epigraph. In particular, for char k = 0, the converse to Steinberg's theorem holds. The existence of a cross-section in G implies, at least for char k = 0, that the algebra k[G]G of class functions on G is generated by rk G elements. We describe, for arbitrary G, a minimal generating set of k[G]G and that of the representation ring of G and answer two Grothendieck's questions on constructing generating sets of k[G]G. We prove the existence of a rational (i.e., local) section of the quotient morphism for arbitrary G and the existence of a rational cross-section in G (for char k = 0, this has been proved earlier); this answers the other question cited in the epigraph. We also prove that the existence of a rational section is equivalent to the existence of a rational W-equivariant map T- - - >G/T where T is a maximal torus of G and W the Weyl group.